Excuse me Euroweenie. The death penalty is about as direct eye for an eye and you are likely to see. This punishment is reserved for the worst of the worst.
Do you not remember John 7:53-8:11, the story of the adultress to be stoned? Jesus was not in favor of capital punishment ("Let he who is without sin cast the first stone."), and was in favor of forgiveness as a general principle.
At that, it's is almost totally unused in the states, with the exception of a few states. An in the cases where it is applied, this is always after numerous expensive appeals.
The death penalty is still in effect in 32 out of 50 states and at the federal level. 3 of the states which banned it recently have not done so retroactively, leaving prisoners still awaiting their execution. While Texas is an extreme outlier for executions, 10 states have had an average of 1 execution per year or more since the penalty was reestablished in 1976. The South as a whole has executed over 1100 people since then.
So we may disagree on this, but to characterize the US as a bunch of death penalty fiends is completely absurd.
And yet we're the only Western country that still has the death penalty; most of the civilized world has given it up. We're also the Western country with (by far) the highest rate of incarceration and the longest prison sentences. We're also one of the few that allows the use of plea bargaining to compel guilty pleas, and many of our states disenfranchise felons, which is also rare in Western democracies. Gallup polls show that 57% of Americans still support the death penalty (down from a peak of around 80% in 1994.)
Over all, we're a very harsh regime when it comes to law enforcement, and the death penalty is just part and parcel of a nation that believes on some level that criminals aren't human and don't deserve to be treated as such. Punishment is part of our culture, not rehabilitation, and certainly not Christian forgiveness.